Version 1.0 Nov. 20, 1992 IAEA Benchmark Problem Based on the Time-of-Flight Experiment on Lead Slabs at FNS/JAERI Hiroshi MAEKAWA and Yukio OYAMA Fusion Reactor Physics Laboratory Department of Reactor Engineering Japan Atomic Energy Research Institute Tokai-mura, Naka-gun, Ibaraki-ken, 319-11 Japan (Phone) 81-292-82-6015 (for H.M.) or -6075 (for Y.O.) (Telefax) 81-292-82-5709 (BITNET) maekawa@fnshp.tokai.jaeri.go.jp (for H.M.) or J3240@fnshp.tokai.jaeri.go.jp (for Y.O.) 1. Numerical Data and Their Format a) Files: PBTG.DAT ------ Source neutron spectrum PB05.DAT ------ 50.8 mm-thick angular neutron flux PB20.DAT ------ 203 mm-thick angular neutron flux PB40.DAT ------ 406 mm-thick angular neutron flux ENERGY.DAT ---- Boundary energy b) Units of the data Source spectrum [n/sr/lethargy/source] Angular flux [n/sr/cm2/lethargy/source] c) Data format for experimental data Comment 1 line 20A4 Energy (mid-point) [MeV] I = 1, 150 6E12.4 Angular flux [See above] I = 1, 150 6E12.4 Error (fraction) [%] I = 1, 150 6E12.4 d) Number of data set PBTG.DAT 1 0 degree PB05.DAT 4 0, 24.9, 42.8, 66.8 degrees PB20.DAT 5 0, 12.2, 24.9, 42.8, 66.8 degrees PB40.DAT 5 0, 12.2, 24.9, 42.8, 66.8 degrees *In the case of 50.8 mm-thick and 12.2-degree, it was revealed that the measured flux was contaminated by some of direct neutrons from the target and too difficult to analysis. Therefore the data of 50.8 mm-thick and 12.2 degree is not included in the file. #The experimental data of 406 mm-thick and 66.8-degree seem to be no good and are for reference. Please don't use for comparison. e) Data format for boundary energy (ENERGY.DAT) Comment 1 line 20A4 Boundary energy [MeV] I = 1, 151 8F9.5 2. Flight Path and Effective Measured Area The flight path and effective measured area are summarized as follows. The meaning of them is described in the references. These data are useful for Monte Carlo calculations. Table Flight path and measured area 50.8 mm-thick Assembly ---------------------------------------------- Angle Flight Path [cm] Measured Area [cm**2] ---------------------------------------------- 0.0 738 85.88 24.9 740 86.34 41.8 744 87.26 66.8 753 89.33 ---------------------------------------------- 203 mm-thick Assembly ---------------------------------------------- Angle Flight Path [cm] Measured Area [cm**2] ---------------------------------------------- 0.0 723 82.42 12.2 724 82.65 24.9 726 83.11 41.8 732 84.49 66.8 746 87.72 ---------------------------------------------- 406 mm-thick Assembly ---------------------------------------------- Angle Flight Path [cm] Measured Area [cm**2] ---------------------------------------------- 0.0 703 77.81 12.2 704 78.04 24.9 708 78.96 41.8 716 80.81 66.8 736 85.41 ---------------------------------------------- 3. Calculational Model The calculational model is of course depend on the code used. Basic data are as follows: Radius of assembly : 31.5 cm Thickness of assembly : 5.08, 20.3 and 40.6 cm Distance between target and assembly : 20 cm Pb atom density : 3.2874x10**22 atoms/cm**3 Area of detector : (pai)x2.54**2 [cm**2] 4. How to Calculate the Angular Flux (1) Neutron source You can use the data of "PBTG.DAT" as the source. Before you start the calculation you should interpolate the spectrum to adjust it to the group structure used. It is notable that the integrated source spectrum multiplied by 4x(pai) is not unity (1.0) but about 1.12. The source neutrons are generated isotropically at the target position. (2) Two-demensional discrete ordinate code such as DOT3.5 You can easily understand from the reference 4) how to do. It is important to average over the measured area when the calculated angular flux is compared with the measured one. (3) Monte Carlo calculation You can see a sample of method in the reference 1). 5. Comparison Two types of comparison will be done for this benchmark problem. (1) To compare the measured and calculated angular fluxes directly in graph. (2) To compare the integrated flux over following four energy regions in C/E values (Ratio of calculated to experimental values); Table Integrated Angular Flux 50.8 mm-thick Assembly ---------------------------------------------------------------------- Energy* 10.183 4.8102 1.9557 0.5070 0.0974 Total [MeV} (14) (29) (47) (74) (107) (>0.0974) Angle --------------------------------------------------------------- 0.0 4.628-4# 0.058-4 0.119-4 0.208-4 0.050-4 5.064-4 (0.076) (12.16) (5.97) (3.45) (14.44) (0.072) 24.9 0.9174-5 0.1096-5 0.449-5 0.790-5 0.183-5 2.451-5 (0.46) (8.02) (2.18) (1.43) (7.25) (0.30) 41.8 0.5176-5 0.1015-5 0.4639-5 0.877-5 0.191-5 2.151-5 (0.70) (7.68) (1.98) (1.30) (7.70) (0.39) 66.8 0.2197-5 0.0923-5 0.4837-5 1.0153-5 0.212-5 2.023-5 (1.11) (6.03) (1.47) (0.90) (5.43) (0.32) ---------------------------------------------------------------------- *Lower energy boundary for each region in MeV and the group number of lower boundary from the higher energy group. #Read as 4.628x10**(-4), (error in %). Table Integrated Angular Flux (Continued) 203 mm-thick Assembly ---------------------------------------------------------------------- Energy* 10.183 4.8102 1.9557 0.5070 0.0974 Total [MeV] (14) (29) (47) (74) (107) (>0.0974) Angle --------------------------------------------------------------- 0.0 5.054-5# 0.106-5 0.337-5 1.176-5 0.404-5 7.071-5 (0.24) (23.31) (7.47) (2.22) (6.73) (0.20) 12.2 1.245-5 0.061-5 0.298-5 1.025-5 0.373-5 3.005-5 (0.46) (19.25) (4.16) (1.35) (4.24) (0.28) 24.9 0.2942-5 0.0491-5 0.283-5 1.0057-5 0.356-5 1.988-5 (0.84) (10.63) (2.17) (0.80) (2.98) (0.30) 41.8 0.1280-5 0.038-5 0.2484-5 0.9406-5 0.345-5 1.704-5 (1.21) (9.18) (1.80) (0.68) (2.64) (0.31) 66.8 0.0348-5 0.0213-5 0.1600-5 0.6634-5 0.2484-5 1.128-5 (4.55) (17.52) (2.99) (0.95) (3.45) (0.44) ---------------------------------------------------------------------- 406 mm-thick Assembly ---------------------------------------------------------------------- Energy* 10.183 4.8102 1.9557 0.5070 0.0974 Total [MeV] (14) (29) (47) (74) (107) (>0.0974) Angle --------------------------------------------------------------- 0.0 2.494-6 0.113-6 0.576-6 3.872-6 2.368-6 9.422-6 (1.01) (46.06) (9.78) (1.74) (3.60) (0.51) 12.2 0.8704-6 0.0707-6 0.4939-6 3.539-6 2.236-6 7.225-6 (1.57) (41.84) (6.99) (1.31) (2.97) (0.54) 24.9 0.3089-6 0.0699-6 0.4514-6 3.4728-6 2.399-6 6.755-6 (3.27) (33.83) (6.73) (1.36) (3.23) (0.72) 41.8 0.1123-6 0.0427-6 0.3384-6 2.8036-6 1.988-6 5.300-6 (7.05) (45.55) (7.68) (1.41) (3.23) (0.75) (66.8 0.1178-6 0.1165-6 0.2218-6 1.7589-6 1.103-6 3.311-6)$ (11.22) (26.43) (16.88) (2.64) (5.74) (1.13) ---------------------------------------------------------------------- *Lower energy boundary for each region in MeV and the group number of lower boundary from the higher energy group. #Read as 5.054x10**(-5), (error in %). $Reference only. 6. References When you publish the results using this numerical data, you should refer at least following references 1) and 2). 1) Oyama Y., Maekawa H.: "Measurement and Analysis of an Angular Neutron Flux on a Beryllium Slab Irradiated with Deuteron-Tritium Neutrons," Nucl. Sci. Eng., 97, 220-234 (1987). 2) Oyama Y., Yamaguchi S., Maekawa H.: "Experimental Results of Angular Neutron Flux Spectra Leaking from Slabs of Fusion Reactor Candidate Materials (I)," JAERI-M 90-092 (1990). 3) Oyama Y., Maekawa H.: "Measurements of Angle-Dependent Neutron Spectra from Lithium-Oxide Slab Assemblies by Time-of-Flight Method," JAERI-M 83-195 (Nov. 1983). 4) Oyama Y., Yamaguchi S., Maekawa H.: "Analysis of Time-of-Flight Experiment on Lithium-Oxide Assemblies by a Two-Dimensional Transport Code DOT3.5," JAERI-M 85-031 (March 1985). 5) Oyama Y., Maekawa H.: "Spectral Measurement of Angular Neutron Flux on the Restricted Surface of Slab Assemblies by the Time-of-Flight Method," Nucl. Instr. Methods, A245 173-181 (1986). 6) Oyama Y., Yamaguchi S., Maekawa H.: "Measurements and Analyses of Angular Neutron Flux Spectra on Graphite and Lithium-Oxide Slabs Irradiated with 14.8 MeV Neutrons," J. Nucl. Sci. Technol., 25, 419-428 (1988). 7) Oyama Y.: "Experimental Study of Angular Neutron Flux Spectra on a Slab Surface to Assess Nuclear Data and Calculational Methods for a Fusion Reactor Design," JAERI-M 88-101 (June 1988). 8) Maekawa H., OYamaY.: "Experiment on Angular Neutron Flux Spectra from Lead Slabs Bombarded by D-T Neutrons," Fusion Eng. Design, 18, 287 (1991). 9) Oyama Y., Maekawa H.: "Experimental Results of Angular Neutron Flux Spectra Leaking from Slabs of Fusion Reactor Candidate Materials (I)," To be published in JAERI-M Report.